Abstract
This paper studies the issue of finite-time performance guaranteed event-triggered (ET) adaptive neural tracking control for strict-feedback nonlinear systems with unknown control direction. A novel finite-time performance function is first constructed to describe the prescribed tracking performance, and then a new lemma is given to show the differentiability and boundedness of the performance function, which is important for the verification of the closed-loop system stability. Furthermore, with the help of the error transformation technique, the origin constrained tracking error is transformed into an equivalent unconstrained one. By utilizing the first-order sliding mode differentiator, the issue of “explosion of complexity” caused by the backstepping design is adequately addressed. Subsequently, an ingenious adaptive updated law is given to co-design the controller and the ET mechanism by the combination of the Nussbaum-type function, thus effectively handling the influences of the measurement error resulted from the ET mechanism and the challenge of the controller design caused by the unknown control direction. The presented event-triggered control scheme can not only guarantee the prescribed tracking performance, but also alleviate the communication burden simultaneously. Finally, numerical and practical examples are provided to demonstrate the validity of the proposed control strategy.
Highlights
In the past decades, strict-feedback nonlinear systems (SFNSs), as a special kind of nonlinear systems, have evoked widespread attention because of their powerful capability to model various kinds of practical systems, such as chemical stirred tank reactor [1], flexible joint robotic system [2], hypersonic flight vehicles [3] and so on
Based on the Nussbaum-type function (NTF) and fuzzy logic approximator, the dynamic surface control (DSC) fuzzy controller presented in [27] has successfully guaranteed the stability of uncertain non-strict-feedback systems with unknown virtual control coefficients
A new lemma is derived to show the differentiability and boundedness of the constructed performance function, which plays an important role for the system stability; 2) A novel adaptive law is given to estimate the upper bound of the actual control gain, and the controller and the ET mechanism are co-designed to compensate successfully the measurement error resulted from the ET mechanism; 3) In combination with such an adaptive law and the hyperbolic tangent function, a novel ET actuator under the relative threshold strategy is proposed, thereby achieving the prescribed finite-time tracking performance and saving the communication resource
Summary
Strict-feedback nonlinear systems (SFNSs), as a special kind of nonlinear systems, have evoked widespread attention because of their powerful capability to model various kinds of practical systems, such as chemical stirred tank reactor [1], flexible joint robotic system [2], hypersonic flight vehicles [3] and so on. Based on the NTF and fuzzy logic approximator, the DSC fuzzy controller presented in [27] has successfully guaranteed the stability of uncertain non-strict-feedback systems with unknown virtual control coefficients These NTF-based results does not concern two hot directions: the prescribed finite time convergence and the limited network resources. A new lemma is derived to show the differentiability and boundedness of the constructed performance function, which plays an important role for the system stability; 2) A novel adaptive law is given to estimate the upper bound of the actual control gain, and the controller and the ET mechanism are co-designed to compensate successfully the measurement error resulted from the ET mechanism; 3) In combination with such an adaptive law and the hyperbolic tangent function, a novel ET actuator under the relative threshold strategy is proposed, thereby achieving the prescribed finite-time tracking performance and saving the communication resource
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